Suppression of seizure in childhood absence epilepsy using robust control of deep brain stimulation: a simulation study

Deep brain stimulation (DBS) is a promising technique to relieve the symptoms in patients with intractable seizures. Although the DBS therapy for seizure suppression dates back more than 40 years, determining stimulation parameters is a significant challenge to the success of this technique. One solution to this challenge with application in a real DBS system is to design a closed-loop control system to regulate the stimulation intensity using computational models of epilepsy automatically. The main goal of the current study is to develop a robust control technique based on adaptive fuzzy terminal sliding mode control (AFTSMC) for eliminating the oscillatory spiking behavior in childhood absence epilepsy (CAE) dynamical model consisting of cortical, thalamic relay, and reticular nuclei neurons. To this end, the membrane voltage dynamics of the three coupled neurons are considered as a three-input three-output nonlinear state delay system. A fuzzy logic system is developed to estimate the unknown nonlinear dynamics of the current and delayed states of the model embedded in the control input. Chattering-free control input (continuous DBS pulses) without any singularity problem is the superiority of the proposed control method. To guarantee the bounded stability of the closed-loop system in a finite time, the upper bounds of the external disturbance and minimum estimation errors are updated online with adaptive laws without any offline tuning phase. Simulation results are provided to show the robustness of AFTSMC in the presence of uncertainty and external disturbances.